Let’s get something straight: Sequestration doesn’t prove that the government is broken or that it can’t get anything done. If anything, it proves the opposite. This is the American government working. Compromising, even.

In summer 2011, both parties came together and agreed that they wanted to reduce the deficit. If they couldn’t compromise on a more appealing policy, then they would use sequestration, which was itself a compromise. The plan called for deep and across-the-board cuts in defense and discretionary domestic spending, with no consideration given to merit. The two parties could, at any moment, choose to end sequestration by passing a one-sentence law repealing it. That they’re not passing that law — or some alternative — is a choice, evidence that the parties prefer sequestration to any other option.

What sequestration proves is that the US government is dumb. There have been three major deficit-reduction packages in the past three years. The first passed in 2011 and set limits on discretionary spending over the next decade. Next came the tax increases in January’s ‘‘fiscal cliff’’ deal, by which part of the tax code reverted to its state before the administration of President George W. Bush. Now we have sequestration, with automatic, across-the-board cuts.

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The total deficit reduction in these three policies is well over $3 trillion, which gets close to stabilizing our debt-to-gross domestic product ratio for the next decade (although not thereafter). What all these policies have in common is that they’re brain-dead ways to reduce the deficit.

Michael Greenstone, an economist at the Massachusetts Institute of Technology and director of the Hamilton Project, anticipated that. So about six months ago, he approached 15 experts and asked them for their best policy proposals, which had to meet two conditions. First, they had to reduce the budget deficit. Second, they had to have ‘‘broader positive effects,’’ such as helping the economy, increasing government efficiency, slowing global warming — that sort of thing. ‘‘The point is we can do good for the budget and do good for the longer-run American economy,’’ Greenstone said.

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The result is ‘‘15 Ways to Rethink the Federal Budget,’’ a 110-page guidebook on how to reduce the deficit.

Perhaps the best and most obvious idea is a carbon tax. Adele Morris, policy director for the Climate and Energy Economics Project at the Brookings Institution, proposes a $16- a-ton carbon tax that would lower the corporate tax rate, include a rebate to low-income households and cut the deficit by about $200 billion over 10 years — all while helping fight global warming, which is a far greater threat than the deficit.

A much milder alternative comes from Harvard University’s Joseph Aldy. He proposes cutting fossil fuel subsidies out of the tax code. That would raise more than $40 billion over the next decade while slightly reducing greenhouse-gas emissions.

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Dana Goldman of the University of Southern California and Michael Chernew of Harvard have a plan to move Medicare to a ‘‘bundled payment’’ system, which would pay medical providers a lump sum for care rather than a per-service fee. There are many devils lurking in the details here — particularly how you measure and share information about the quality of care — but if managed well, the changeover could save $100 billion while giving providers a much-needed reason to begin managing disease and disability in a coordinated way.

Speaking of disability, Harvard’s Jeffrey Liebman and the Office of Management and Budget’s Jack Smalligan propose three projects to test ways to reconfigure the disability system to help injured workers get back to work sooner and in better health. The ideas wouldn’t save much in the next decade — $10 billion to $15 billion, the authors estimate — but if they produced a better disability system, the long-term dividends could be huge for both workers and the budget.

Diane Lim, the chief economist at Pew Charitable Trusts, proposes converting the various deductions in the tax code to 15 percent, nonrefundable tax credits. The resulting tax code would be simpler and much more progressive. Oh, and it would raise $2.7 trillion, much of which we could use to lower marginal tax rates.

Pia Orrenius and Madeline Zavodny, of the American Enterprise Institute, and Giovanni Peri, of the University of California at Davis, have an innovative proposal to auction off temporary work visas, which would help allocate them more efficiently while raising $7 billion to $12 billion for the federal government. If the system worked, it would also provide valuable information — through rising or falling visa prices at auction — about the demand for foreign workers and thus how to set the parameters of our immigration system.

The point isn’t that each and every one of the Hamilton Project’s ideas is great. It’s that each is an attempt to formulate intelligent policy that will make the country better as it makes the deficit smaller. That’s a far cry from sequestration — and the past few years of policymaking generally — in which Washington appears to have resigned itself to deficit reduction of almost exclusively bad and dumb ideas.